Problem: Rewrite as a simplified fraction. ${3.70\overline{4} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 3704.4444...\\ 100x &= 370.4444...\end{align*}}$ Subtracting the two equations, we have: ${900x = 3334}$ ${x = \dfrac{3334}{900}} $ ${x = \dfrac{1667}{450}} \text{or} {3 \dfrac{317}{450}}$